Gear Ratio Selection
 

I am in the process of selecting a new set of gear ratios for my bike. I used to use a process that involved plotting the ratios on a graph and selecting gears and chainwheels using the results - a graphical analysis.

Can someone refresh my memory on how to do this and what to look for?

Here is what I remember. Perhaps you can look this over and correct as necessary.

1. Calculate the gear ratio (or inches of travel per crank turn if you are also considering wheel size in the trade space).

2. Calculate the logarithm of the ratios.

3. Plot the ratios on a number line.

4. Review your data

Selection Criteria -

a) Evenly spaced ratios from lowest to highest, preferably with no duplication(s).

b) Reasonable shifting patterns, preferably a repetitious pattern.

c) Rear gear sizes that can handled by the derailleur.

d) Front chain ring sizes that can be handled by the front derailleur.


If I have this correct, what do you think is the largest ratio step size that is practical (smooth, useful) and worth going up or down to get)?

As an add-on to the above, I just went through this process. Here's what I got:

47/50T chainrings
Nuovo Record front derailleur - should be a piece of cake for range, shifting ease and no chain rub even at the extremes of the ranges.

13, 15, 17, 20, 23, 26T freewheel
Nuovo Record rear derailleur - I'm a little concerned about 26T cog but I'm going to try it out and see how it goes.

This table shows the ratios. You can also see the shifting pattern.

rear...frt...gear
cog....ring...ratio
26...47...1.69
26...50...1.72
23...47...1.74
23...50...1.77
20...47...1.80
20....50..1.83
17...47...1.87
17...50...1.90
15...47...1.93
15...50...1.95
13...47...1.99
13...50...2.02

This is also a decent shifting pattern - single shift then double shift.


What do you think? Do I have this right? I "know" several of these ratios like old friends, so those are good to go. The real question is what about the others? In my opinion, the all-too-common 42/52T chainring pair never worked all that well for me. Vintage freewheels and chainrings aren't cheap, so I don't want to make a mistake.

Here's another that looks even better. There seems to be some "magic" with a three-tooth difference in front chain rings.

25... 47... 1.71
25... 50... 1.73
22... 47... 1.76
22... 50... 1.79
19... 47... 1.82
19... 50... 1.85
17... 47... 1.87
17... 50... 1.90
15... 47... 1.93
15... 50... 1.95
13... 47... 1.99
13... 50... 2.02

this tool may help accelerate your calculations: http://www.velobase.com/Resource_Tools/GearCalc.aspx

http://www.panix.com/~jbarrm/cycal/cycal.30f.html
personally, I like this one better.

I was researching the archives of this web site minimg for info. The gear shift pattern above is apparently called a "half step". I guess I knew that in the past, I just could not remember the name for it.

The name "half step" derives from the chainring shift making half as much change in ratio as a rear cog shift.

I will check out those web sites later tonight.

Mike, your half-steps look perfect to me. What's fun about them is that you can change just the inner chainring to convert to a 1.5-step for hill work, viz:

50-47 / 14-16-18-20-23-26, similar to what you posted above
50-42 / 14-16-18-20-23-26, for a lower bottom gear, at the cost of a gap at the top and the bottom

The latter is what I normally run on my Bianchi. Capo #2 is getting a similar half-step:
49-46 / 14-16-18-21-24-26 (or ... 18-20-23-26, but I want the lower gears)

If you need a bit more range, half-step-plus-granny can be pretty cool:
48-45-34 / 13-15-17-19-21-24 (run that through your Excel spreadsheet)

There are some good combinations for 52-42. One popular choice was 14-16-18-21-24; another, for the truly hard-core, was 14-15-16-17-18. I have much better luck with either 52-44, 50-42, or 48-40, because these work so nicely with a 2-tooth progression in back. You might like my mountain bike gearing: 48-40-24 / 13-15-17-19-22-24-26 (or 28)

Lots of numbers...and isn't that an awful lot to think about?
How does that translate to real-time riding?
Do you actually shift twice each step?
I had no clue....obviously.

I ride the big ring unless it gets too hard, then I go small.
I know that's a simplistic view, but I almost never use the small cogs on the small ring.
I'm either climbing or going as fast as possible.
I am starting to realize the value of steady cadence, sometimes.

I guess what I'm asking is, how would knowing that information make me faster in say, a triathlon?

I'll take my answer off the air.

John E,

I used to have a 13-15-17-19-21 X 42/52. IIRC, even in my prime, I used to have trouble pushing a 52-15 for very long without drafting someone.

I wish my frame would accommodate a triple crank but I believe it is too tight for that - short chain stays, etc. I'm okay with the combinations I listed above. At least for now. As you know, California is pretty flat here by the ocean.

This is a REALLY nice bike. I need to it put back together and get back out there. I'm waiting on brake cable housings then I'm on the road again - can't go anywhere without brakes!

Robbie,

Numbers are what I do for a living. I enjoy numbers. I understand numbers the way some people understand spoken languages.

The thing is, I've ridden bicycles long enough to know exactly what each of those combinations feels like. I know from long experience (numbers and riding) that I want a ratio of X (say, 52X17) because I know that's what is good for this stretch of flats but it's too big for hill climbing and too small for drafting. I need a bike that has the right gears, so that when I reach for more (or less) I have the exact amount at hand and I know where it is. I don't even have to think about the shift. I bump (or pull) the front derailleur and add (or subtract) one from the rear. It does not require much thought. I just do it.

I hated it when I wanted X but could only get Y (too much) or Z (too little). As I get older, it becomes increasingly important to me. Remember, I am also vintage now, not just my bike.

Those of you with ten speed cassettes spaced one tooth a part and double (or triple) chainrings probably have a hard time understanding the need to plan ahead like this. You may have no idea how easy it is to just click shift as opposed to overshift and come back the exact amount without too much thought. When you have a Nuovo Record friction shifter, you learn these things. When you have only five in the rear, it pays to plan ahead.

It is quite simple for those of us who grew up with 1/2-step and 1.5-step gearing, which were ubiquitous in the 1950s and 1960s and into the early 1970s. As I accelerate and need to "go through the gears," I normally shift the right lever one cog (two ratios) at a time, going up through either the even- or the odd-numbered gears. Then, as I reach cruising speed and want a finer adjustment, I shift the left lever, which always takes me from a given ratio to the next higher (pulling the lever back) or lower (pushing the lever forward) gear. Double shifts are easily accomplished with barcons or by grabbing both downtube levers at once. Operating a 1.5-step combination takes slightly more concentration, because the left lever now provides a 3-ratio change to the right lever's two-ratio change, but even that gets pretty easy and near-automatic with a little practice.

As was pointed out, as soon as one gets to 9 or 10 cogs with corncob spacing at least at the high end, shifting becomes even easier to figure out, although I still see plenty of folks cross-chaining because they don't know how to obtain the same ratio on the other chainring, with a much better chainline.

...exactly what I'm missing, I think. I ride 12t-19t 8-sp on 3 bikes, with 53/39 up front, 172.5 cranks, so when I switch bikes it's about the same ride. My goal is not a cadence, in general, but to get back to 53/12t absolutely as soon as possible after a corner or hill. Corners aren't so hard, once you figure out how to carry speed through the line. I figure I'm missing something as I approach hills, because I'm only able to get "ahead" of the hill about 20% of the time. Getting "behind" the hill is a real pain in the acid (lactic) to overcome.

I'll take what I see here, do some more trial and error. I guess I'll have to chart my stuff first.
Thanks.

Robbie,

53X12 = lol (for me) Enjoy it while you can.

For me, that would be like slogging and grinding instead of riding/spinning. I suppose, if I were drafting someone, then yes, otherwise fahgedaboudit!

Now, if you get into 53X12 ASAP during normal riding, why then is this your top gear? What do you do when you have a tail wind or a slight down hill, coast? Robbie, I know nothing about you as a rider. I think you should gear down a bit and spin rather than grind. I could be totally wrong. Let me know.

awesome for those of you who can plot out your ratios and shift paterns. makes sense and good for you. for me, if i get off my single speed bike to ride a multispeed bike, and its not a 3speed, i have a much more pleasurable time thinking of it like ranges. big chainring up front for flats and downhills, shifting thru whatever i have on the rear (i do appreciate a tight ratio rear cluster at times) and the middle ring for cruising around and the small chainring for trails and off road technical or hills. love my rear gears and use them alot, i just don't see why to shift back and forth thru the large chainring, or any of them for most the time riding.

i know this is seen as wrong, but isn't it just for the enjoyment of the ride that we ride?

You're not the first person to tell me to gear down and spin, and I'm sure you're right. It's hard to do that, though. As a 5k, 10k, and even marathoner, I simply ran as hard as I could most of the time. This seems to be carrying over into my cycling.

Maybe it's time constraints, or something, but I try to get a good workout inside the time I have, which is often an hour, so I go as hard as I can. With other riders, I pretty much ride their pace and look around. On downhills and with tailwinds, I'm still like a kid, gotta go as fast as possible.

Logically, I figured that at least some of the small ring / small cogs would be equivalent to the big ring / big cogs, I just thought I'd be busy shifting and nearly duplicating the ratio, and thought, "why bother?"

I've eyeballed your charting, and will try to create my own. I have a Kestrel freak friend who has no time for C&V, but actually emailed me a chart like that once, and I deleted it because it made no sense at the time. I think I'll revisit the idea and give it a couple of weeks, see what happens.

Thanks for the advice. I'm learning, and appreciate your time.

Robbie, honestly, with eight cogs in the rear it doesn't really matter. I already plotted yours up on my computer.

Mike, as a fellow numbers freak, it's great to see your methodology. Here's what I do: Decide what my top gear and bottom gear rations will be, based on riding style and on hardware constraints, like what do I have in the toybox?

If there's a convenient choice of chainwheels (i.e. I have a 53/39 and don't want to change it out), I pick the small cog that will give me the top gear and the big cog that will give the bottom gear. Then I take the ratio of these two cogs, and decide how many cogs there will be in the rear. Recently I've played with 10 speed. If n=10, find the n-1 root of that ratio. This is the ideal factorial step between rear cogs. Now convert this series into integers by rounding, and see if the tooth count progression looks as smooth and even-tempered as can be. You could see this by plotting the log of the integral tooth ratios with the ideal factorial ratio. then play with the tooth counts to see if you can get another even spread that is more even.

Then lay the pattern out in a table, crankset teeth the abcissa and cogset teeth the ordinate, and map out the shift pattern with tooth jumps. Again you can see, now across the whole pattern, if there are major inconsistencies. Saying when it's good is a judgement call.

There's an old phrase, sometimes you need to shoot the engineer and take the work to production.

Road Fan

LOL!

Then again, if you have a ten speed freewheel in the rear you don't even need to look at this thread. Just have a one tooth jump from smallest to largest and go ride.

If you want a narrow spread, yes, but if you're setting up a 2X10 standard or compact, or if you want a triple that has the most usable gears with spread, you can't just go with a straight block.

But shift patterns become more straightforward. Just nicking up and down the cogs with a chainwheel shift when the chain angle becomes extreme, is called a crossover. Simpler to drive than a half-step or 1.5-step (aka Alpine), that's why they're more popular now. I think the most elegant is a widish range half-step 10 - I nearly bought a Urago with that, and am still kicking myself!!

Road Fan

It must be karma.

Today, screaming along on my Ti, playing little games with merging traffic, I received my comeuppance.

The FD decided, for some reason, to drop the chain off the big ring onto the small ring. No amount of pull would bring it back, so I finished the last 3 miles on the small ring. Dazed and confused. My crash course in small ring riding was not fun, way too much chain rub on my favorite cogs, and I was doing a lot of FD trimming.

When I got home, I re-adjusted a bike that for the last two weeks was spot-on, and of course it threw the chain over the top and scratched up my crank arm. That's a different thread.

I'm going to take a stab at the ratios and see what's up. I've decided to try it 2x a week on my steel Ironman, then go from there.

That sounds pretty stout to me too. Although after one of the time trials in last summer's TDF, I heard one of the riders complain that he kept spinning out in his top gear, which, as I recall, was something like 55x11. Dare to dream.

I may run that combo as much as possible, but it's not like I'm turning 70 rpm or anything on it. I"m trying to follow Mike's advice and spin up. I really like the 12-19 set-up. Eastern NC where I'm at is just not really inclined, and this county has smooth backroads. Other than wind, the only obstacle is me engine.

I used to drive my friend's Le Car with the hatch open, and he'd draft under it to train for TT's and tri's.
Can't do that with hills around.

I can tell you're trying to be charitable. But the fact is, I live in the flatlands and there's still no way I could push that gear. I have a 53/42 with a 14-19 rear. I'm almost never in anything bigger than 53-17, and I probably spend 90% of my time on either the 42-15 or 53-18. I guess my engine is a bigger obstacle than yours, or I have a lower pain threshold.

If you like numbers....

The magic one is 0.002975 (IIRC).
Multiply that by gear inches by cadence to get MPH.
Know what MPH you want to cruise at (16? 18? 20!? 23!!!?) and set up one of the middle cogs on the big ring to give that in gear inches at the cadence you normally like to ride.
This gives you some leeway for headwinds & tailwinds, plus the bottom ring for hills.

It's a little different approach.

Also, be leery of getting locked into thinking about it as a "52x17" or whatever, as that has a different meaning on a bike with 650c, 700c, and 27" wheels, and especially Moultons (this is C&V after all).